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Course: AAE 340, Spring 2012
School: Purdue
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Word Count: 385

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340 AAE Dynamics and Vibrations Problem Set 1 Due: 9/18/2012 On the 340 Blackboard site, a review of dimensions is included in a document: Supplementary Material 203 Review Material Dimensional Analysis. After reading the document, consider the following problems: Problem 1: Determine the appropriate dimensions in these examples. (a) A particle moves under the influence of two forces such that its location is...

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340 AAE Dynamics and Vibrations Problem Set 1 Due: 9/18/2012 On the 340 Blackboard site, a review of dimensions is included in a document: Supplementary Material 203 Review Material Dimensional Analysis. After reading the document, consider the following problems: Problem 1: Determine the appropriate dimensions in these examples. (a) A particle moves under the influence of two forces such that its location is determined from the following relationship y m s ln 1 s k Given dim y L, dim m M , and dim s L , determine the dimensions of , k , . T (b) The following equation describes motions of a spacecraft in orbit G 2 dx u 2Gq qH 2 1 3sin Gq c 0 where G 2 dy dt D D y0 Assume 1 F dim H T L dim q L dim D L M dim dim c F L dim u Determine the dimensions of , , , y and x . y1 Problem 2: A mechanism is comprised of two rigid bars OS (length h) and SU (length ) that move in the same plane and are pinned at O and S. Unit vectors are defined such that ei are inertially-fixed, a are fixed in bar OS b and are fixed in bar SU. k j b1 e3 S e2 b3 a1 a2 U O (a) Derive the unit vector relationships, that is, write unit vectors a1 , a2 , a3 in terms of both e , e , e and b , b , b . 1 2 3 1 2 3 Write b1 , b2 , b3 in terms of e1 , e2 , e3 . Express the angular velocities e a , a b . (b) The motion of interest is the path of S. Thus, point S is the terminal point of a position vector. But consider two different base points: O and U. Write position vectors r OS and r US and express each in terms of a1 , a2 , a3 . The motion of point S can be viewed by different observers as well. Write expressions for the following quantities: ev OS , a v OS , b v OS , e v US , a v US , b v US . Express each velocity in terms of a1 , a2 , a3 . Which velocities are generic? How do you know? Ans : e v OS h a2 e US v b1 sin a1 cos a2 (c) Let h 1 met, = 0.5 met. At a certain instant, 45 , .5rad / s, = 30 , .2rad / s . Evaluate the velocities in (b) and determine the speed for each. Are they the same?
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Purdue - AAE - 340
Purdue - AAE - 340
AAE 340 Dynamics and VibrationsProblem Set 2Due: 1/25/20121. A particle P moves on the Spiral of Archimedes at a constant speed 2 met/s as shownbelow. The equation governing the spiral is r 3 .urn3On2u(a) Let n be inertially fixed unit vectors.
Purdue - AAE - 340
AAE 340 Dynamics and VibrationsProblem Set 3Due: 2/1/12Problem 1: The mass particle in the figure is suspended from a linear spring of constantk, with an unstretched length o . Define as the position of the particle with respect tothe unstretched pos
Purdue - AAE - 340
Purdue - AAE - 340
AAE 340 Dynamics and VibrationsProblem Set 4Due: 2/10/12Problem 1: A particle of mass m is free to move on the smooth surface. Attached is aspring of constant k and dashpot of constant c. An external force acts; it is selected to beof the form f ( t
Purdue - AAE - 340
AAE 340 Dynamics and VibrationsProblem Set 5Due: 2/17/12Problem 1: Below a particle of mass m is fixed to the end of a massless L-shaped rod. Aspring and a dashpot are attached. The rod can pivot in a vertical plane. In the positionindicated, the sys
Purdue - AAE - 340
AAE 340 Dynamics and VibrationsProblem Set 6Due: 2/24/121. A simple pendulum of length L and mass m appears below.Let m = 2 kg and L = 8 meters.gL(a) Assume small oscillations and derive the EOM.At the initial time, (0) 150 , (0) 0 . Determine the
Purdue - AAE - 340
AAE 340 Dynamics and VibrationsProblem Set 7Due: 3/1/12Problem 1: The system below consists of two identical particles at the ends of a rigid,massless L-shaped rod. The short and long arms of the rod have lengths and L,respectively. The rod can pivot
Purdue - AAE - 340
AAE 340 Dynamics and VibrationsProblem Set 9Due: 3/26/12Problem 1: The system below consists of two particles A and B of equal mass mconnected by a rigid, massless rod. One particle is attached by a pin to the end of amassless T-bar. The rod is free
Purdue - AAE - 340
AAE 340 Dynamics and VibrationsProblem Set 10Due: 4/2/12Problem 1: For an aircraft, assume that unit vectors i are inertial (fixed in the ground)and the body-fixed unit vectors are b .(a) The angles yaw, pitch, and roll represent the rotational degre
Purdue - AAE - 340
Instructors Solutions Manualto accompanyFundamentals of AerodynamicsFourth EditionJohn D. Anderson, Jr.Curator of AerodynamicsNational Air and Space MuseumandProfessor EmeritusUniversity of MarylandPROPRIETARY AND CONFIDENTIALThis Manual is the
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EEL 4930/6447Laser ElectronicsUpdated:1/10/12 16:23 2011 Henry ZmudaSet 0 Introduction1Laser Electronics (EEL 4930/6447) - 3 CreditsSpring Semester 2012Meeting Time/Place:MWF, 3rd (9:35 10:25) Benton 328Instructor:Office:Office Phone:Cell Pho
University of Florida - EEL - 6447
Gaussian Beam Optics,Ray Tracing, and CavitiesRevised: 1/25/12 1:57 PM 2011, Henry ZmudaSet 1 Gaussian Beams and Optical Cavities1I. Gaussian Beams(Text Chapter 3) 2011, Henry ZmudaSet 1 Gaussian Beams and Optical Cavities2Gaussian BeamsReal o
University of Florida - EEL - 6447
Atomic RadiationRevised: 2/9/12 10:44 2011, Henry ZmudaSet 2 Atomic Radiation1Atomic RadiationA laser is a quantum device.Energy levels in an atomic system are discrete, be theymolecular, solid, or semiconductor.( 2)(1)EnergyLevelDiagram 201
University of Florida - EEL - 6447
Laser Oscillation &amp; AmplificationRevised: 2/2/12 17:02 2011, Henry ZmudaSet 3 Laser Oscillation1Threshold ConditionsFrom Slide 50 of Note set 2, our central equation of lasertheory, we recall:&quot;&quot;2g2 %! o ( f ) = g ( f ) 2 A21 \$ N 2 ! N1 '8n #g
University of Florida - EEL - 6447
Laser CharacteristicsRevised: 3/21/12 13:04 2012, Henry ZmudaSet 4 Laser Characteristics1Laser CharacteristicsStill to be answered:1. What is the laser amplitude?2. What if there are transient effects (time dynamics)?3. What exactly is the pumpin
University of Florida - EEL - 6447
Mode Locked LasersRevised: 2/24/12 10:56 2011, Henry ZmudaSet 4a Mode Locked Lasers1Mode Locked Lasers 2011, Henry ZmudaSet 4a Mode Locked Lasers2Mode Locked Lasers 2011, Henry ZmudaSet 4a Mode Locked Lasers3Mode Locked Lasers 2011, Henry Zm
University of Florida - EEL - 6447
Pulsed LasersRevised: 3/21/12 13:28 2012, Henry ZmudaSet 5a Pulsed Lasers1Laser Dynamics Puled LasersMore efficient pulsing schemes are based on turning thelaser itself on and off by means of an internal modulationprocess, designed so that energy
University of Florida - EEL - 6447
Semiconductor LasersRevised: 3/21/12 12:56 2012, Henry ZmudaSet 6 Semiconductor Laser Fundamentals1Semiconductor LasersThe simplest laser of all. 2012, Henry ZmudaSet 6 Semiconductor Laser Fundamentals2Semiconductor LasersThe simplest laser of
University of Florida - EEL - 6447
Laser DiodesRevised: 3/27/12 15:24 2012, Henry ZmudaSet 6a Laser Diodes1Semiconductor LasersThe simplest laser of all. 2012, Henry ZmudaSet 6a Laser Diodes2Semiconductor Lasers1. Homojunction Lasers2. Heterojunction Lasers3. Quantum Well Lase
University of Florida - EEL - 6487
Vector PotentialsSet 1 - Vector Potentials1Maxwell s Equations Time-Harmonic Electromagnetic Fields Homogeneous Medium!!! &quot; E = # j\$ H # M!!! &quot; H = j\$% E + J!&amp;!i E =%! &amp;m!i H =Set 1 - Vector Potentials2The Wave Equation Time-Harmonic Fie
University of Florida - EEL - 6487
Radiation and ScatteringSet 2 Radiation and Scattering1The Near Field: Recall,z( x, y, z)! r! r!A=4!!R!e &quot; j !R#V# J x !, y !, z ! R dv !( x, y , z )()! !R = R = r !r&quot;yxSet 2 Radiation and Scattering2!!e ! j !RA=!V! J x !, y !
University of Florida - EEL - 6487
Planar ScatteringSet 3 Planar Scattering1Radiation form an infinite line source.yxIezSet 3 Planar Scattering2!I e ( z !) = a z I eRecall:!e &quot; j !RA=# I e x !, y !, z ! R d ! !4! C&quot;\$ A = a z Az ! , &quot; , z()()!!e &quot; j !RF=# I m x !
University of Florida - EEL - 6487
Cylindrical ScatteringSet 4 Cylindrical Scattering1For scattering of a plane wave from a planar surface, rectangularcoordinates provided the most convenient basis. For scatteringfrom cylindrical structures, the plane wave is best described interms o
University of Florida - EEL - 6487
RECTANGULAR WAVEGUIDESSet 5 - Rectangular Waveguide1Maxwells Equations:= j is assumed, region is also assumed source free.t E = j HEz E y= oHx jyzEx Ez= oH y jzxE y Ex= oHz jxy H = j EH z H y=xj EyzH x H z=yj EzxH y H x=z
University of Florida - EEL - 6487
Cylindrical Scattering ContinuedScattering by a (Two-Dimensional)Conducting WedgeSet 5 - Scattering by a Conducting Wedge1Infinitely long electric currentTMz PolarizationIeyxzSet 5 - Scattering by a Conducting Wedge2Incident electric field pr
University of Florida - EEL - 6487
CIRCULAR (ROUND) WAVEGUIDESSet 6 - Round Waveguide1 =az0zaazaSet 6 - Round Waveguide2Maxwells Equations:= jtassumed E = j H1 Ez E= oH j zE Ez= o H jz1 ( E ) E = oHz j H = j E1 H z Hj E= zH H z=j Ez1 ( H ) H Set 6
University of Florida - EEL - 6487
Scattering by a Conducting SphereSet 6 - Scattering by a Conducting Sphere1zSphericalCoordinatesA quick review from last semester.arzoo( xo , yo , zo )aroayooyxoxSet 6 - Scattering by a Conducting Sphere2The Wave Equation Time-Harmoni
University of Florida - EEL - 6487
Integral Equationsand theMethod of MomentsSet 7 - Integral Equations and the Method of Moments - Part 11Integral Equation Method Objective: Express the(unknown) current density induced on the surface of ascattering object in the form of an integral
University of Florida - EEL - 6487
Electric Field Integral Equation(EFIE)Set 8 - Integral Equations and the Method of Moments Part 21In general the EFIE is based on the fact that the satisfaction ofboundary conditions requires that the total tangential electricfield on the surface of
University of Florida - EEL - 6487
Spectral Domain TechniquesandDiffraction TheorySet 9 - Spectral Domain Techniques and Diffraction Theory - 2-D Fields1References:1. *R.H. Clark and J. Brown, Diffraction Theory andAntennas, Wiley, 1980 Excellent treatment, easy to read.2. P.C. Cle
University of Florida - EEL - 6487
Review of Electromagnetic Field TheorySet 1 - Review of Fundamental Electromagnetic Field Theory1Maxwells Equations Differential Form Time Domain E (r ,t ) = B ( r , t )tD ( r , t ) M (r ,t ) H (r ,t )=+ J (r ,t )tD ( r , t ) = (r ,t )(B (
University of Florida - EEL - 6487
The Wave EquationSet 2 - The Wave Equation1The Wave EquationH E E = M, H = +JttH E = Mt= H Mt E = + J Mt t2E= 2 J MttSet 2 - The Wave Equation2The Wave Equation2 A = A A2E2 E = E E = 2 J MttD = E = J JS + E=2JS
University of Florida - EEL - 6487
Spectral Domain TechniquesandDiffraction TheoryThree-Dimensional FieldsSet 10 - Spectral Domain Techniques and Diffraction Theory 3-D Fields1Three Dimensional FieldsAngular spectrum for linearly polarized aperture fields.xAperture AzyThe radia
University of Florida - EEL - 6487
EEL 6487Instructor:ELECTROMAGNETIC FIELD THEORY II Spring 2012Prof. Henry Zmuda235 Larsen Hall(352) 392 0990 (Office)(850) 225 9200 (Cell - Emergencies only please!)zmuda@ece.ufl.eduText: C.A. Balanis, Advanced Engineering Electromagnetics, John W
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EEL 3211 Homework 2 Solutions
University of Florida - EEL - 3211
EEL 3211 Homework 4 Solutions Chapter 4 Assignment: Problems 4-2, 4-3, 4-4, 4-5
University of Florida - EEL - 5441
EEL 4458/5441Fundamentals of PhotonicsUpdated:8/18/11 14:01 2011 Henry ZmudaSet 0 Introduction1Fundamentals of Photonics (EEL 4458/5441) - 3 CreditsSpring Semester 2011Meeting Time/Place:MWF, 3rd (9:35 10:25) Larsen 330Instructor:Office:Office
University of Florida - EEL - 5441
Essentials of Electromagnetic Field TheoryMaxwells equations serve as a fundamentaltool in photonicsUpdated: 9/8/11 11:52 2011, Henry Zmuda - Essentials of Electromagnetic Theory for Photonics1Light is an Electromagnetic WaveElectromagnetic waves a
University of Florida - EEL - 5441
Rectangular Dielectric Waveguide(Revised 9/21/11) 2011 Henry ZmudaSet 10 - Rectangular Dielectric Waveguides1Rectangular Dielectric Waveguide(Revised 9/21/11)Side View!kncGuided WaveConfined in xdirectionxCovernfGuiding FilmnsSubstratey
University of Florida - EEL - 5441
The Planar Slab WaveguideBasic Optical WireRevised: 9/14/11 15:38 2011, Henry ZmudaSet 2 Planar Slab Waveguide1The Infinite Slab Waveguide Simplest OpticalWaveguide Structuren f &gt; ns &gt; ncxncCoverGuiding FilmnfSubstrateyznsSinusoidal stea
University of Florida - EEL - 5441
Dispersion in Optical WaveguidesUpdated: 10/4/11 14:29 2011 Henry ZmudaSet 3 - Dispersion1Dispersion:Motivation for using optical waveguides is the large information capacity(large bandwidth).What are the bandwidth limitationsof optical waveguide
University of Florida - EEL - 5441
Graded-Index WaveguidesUpdated: 9/8/11 10:47 2011 Henry ZmudaSet 3 - Graded-Index Waveguides1Graded-Index WaveguidesTwo ways to to reduce modal dispersion:1. Use a single mode waveguide2. Use a graded-index waveguidencncnfnsnfnsMulti ModeS
University of Florida - EEL - 5441
Optical Detection and NoiseUpdated: 11/16/11 10:46 2011 Henry ZmudaSet 7 - Detection and Noise1Detection ProcessOptical electrical conversion/detection is a critical process.The optimum detector depends on wavelength, informationbandwidth, and opt
University of Florida - EEL - 5441
Optical DetectorsUpdated: 11/22/11 09:21 2011 Henry ZmudaSet 8 - Detectors1Optical DetectorsWe focus on junction semiconductor detectorsFour basic parameters used to characterize detectors1. Responsivity: Amount of electrical signal obtained per u
University of Florida - EEL - 5441
ANTI REFLECTION (AR) COATINGSand MULTILAYER FILMS forHIGH REFLECTIVITY DIELECTRIC MIRRORSDiscussion based on:E. Hecht, Optics (2nd Ed.) Addison Wesley, 1987, pp. 373 378. 2011 Henry ZmudaAR Coatings1Remember this side? Note Set 1, Slide 27: 2 , 2
University of Florida - EEL - 5441
Optical ModulatorsUpdated: 11/22/11 09:24 2011 Henry ZmudaSet 9 - Modulators1Optical ModulatorsModulators are the means by which information is encoded ontothe optical carrier.There are two basic forms of modulation:1. Direct Modulation2. Extern
University of Florida - EEL - 5441
Pollock Problems 1, 4 (Dispersion Chapter) V12!3.52 # 3.42 = 3.69 : There are about 4 TE modes and 4 TM 1. a) m ! = &quot; 2 &quot;!0.9 modes, so modal dispersion is an issue. b) The Group Delay Dispersion depends on di
University of Florida - EEL - 5441
Step-Index Circular Waveguide(Dielectric Rod Waveguide, Optical Fiber)Updated: 10/3/11 13:21 2011 Henry ZmudaSet 5 - Optical Fiber1Step-Index Circular WaveguideJacketBufferCladdingCore 2011 Henry ZmudaCladdingCoreSet 5 - Optical Fiber2Step
University of Florida - EEL - 5441
Problem 2.2 %#2! ( ! E &quot; ! 2 E = &quot;! ' E \$!*&amp;)#t2 Let E ( z, t ) = Z ( z ) T (t ) , then #! (%Z !T &quot; ! ZT ! = &quot;# ' ZT \$*&amp;!)# \$ #! (% #!= T ' Z!+Z*&amp;!!)Divide both side by ZT , Z !T ! Z ! #!&quot; !=+ZTZ!# \$ #
University of Florida - EEL - 5441
Attenuation and Nonlinear EffectsUpdated: 10/3/11 13:22 2011 Henry ZmudaSet 6 - Attenuation and Nonlinear Effects1Attenuation and Nonlinear EffectsAn optical signal degrades by attenuation and dispersion as it propagatesthrough a material.Dispersi
University of Florida - EEL - 5441
Numerical Aperture for a graded index fiber: For graded index waveguides, the NA is a function of position on the waveguide endface. A ray entering the endface must turn parallel the zaxis before it reaches the li
University of Florida - EEL - 5441
Problem 2.7 The fields in the two regains are given by: Einc = Eo e jko ( z cos 45! y sin 45)e j&quot; t Eref = rEo e jko ( ! z cos 45! y sin 45)e j&quot; t Etrans = ! Eo e jko ( z cos&quot;2 # y sin&quot;2 )e j\$ t The refraction angle is f
University of Florida - EEL - 5441
University of Florida - EEL - 5441
Problem 3-4DIELECTRIC SLAB WAVEGUIDEn c := 1.0n f := 1.56h := 7 10n s := 1.4786o := 1 10()fmax k o := k o k o :=2 oco := 3 10k omax := 1.25 k o6k o = 6.283 10 n 2 n 2sfs f :=() n 2 n 2 k 2 2s off() n 2 n 2 k 2 2c offc f :=
University of Florida - EEL - 5441
Problem 3-11DIELECTRIC SLAB WAVEGUIDEn c := 1.0n f := 1.56h := 2 10n s := 1.488o := 1.3 106()fmax k o := k o k o :=co := 3 102 k omax := 1.25 k oo6k o = 4.833 10 n 2 n 2sfs f :=() n 2 n 2 k 2 2s off() n 2 n 2 k 2 2c offc f
Pittsburgh - ECON - 0100
ECON 1100: Intermediate MicroeconomicsInstructor: Sandra Orozco1. In the ancient country of Roma, only two goods, spaghetti and meatballs, are produced.There are two tribes in Roma, the Tivoli and the Frivoli. By themselves, the Tivoli eachmonth can p
Pittsburgh - ECON - 0100
Chapter 9 Costo Explicit cost- a cost that involves actually laying out moneyo Implicit cost- does not require an outlay of money; measured by the valueof the benefits that are foregoneo Sunk cost- cost that has already been incurred and is non-recov
Pittsburgh - ECON - 0100
Micro Midterm 1Chapter 1 Economic analysis is based on a set of common principleso Principles for understanding the economics of how individuals makechoices Individual choice- the decision by an individual of what to dowhich necessarily involves a d
Pittsburgh - HIST - 101
770-96 Competing Alliances, Clashing Ambitions Imperial competition causes rivalries to intensify among the Powersnationalism &quot;Arms race&quot; among superpowers stimulates economies but will haunt the future Dual Alliance: between new German empire and Austria
Pittsburgh - HIST - 101
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